SPT+Planck Compton-y Maps Overview

• The paper introduces SPT+Planck Compton-y maps that combine high-resolution SPT data with Planck’s full-sky coverage to accurately trace the thermal Sunyaev–Zel’dovich effect.
• It details a multi-frequency, harmonic-space component separation methodology that minimizes noise and foreground contamination using inverse noise variance weighting and specialized filtering.
• The resulting maps enable high-fidelity studies of intracluster pressure profiles, cosmic baryon distribution, and CMB secondary anisotropies, advancing precision cosmology.

The SPT+Planck Compton-y maps are specialized astrophysical data products designed to trace the thermal Sunyaev–Zel’dovich (tSZ) effect, which encodes the integrated thermal pressure along the line of sight from clusters, groups, and diffuse large-scale structure gas. These maps are constructed by optimally combining South Pole Telescope (SPT) data—characterized by high angular resolution and low instrumental noise at arcminute scales—with Planck satellite data, which provide full-sky coverage and sensitivity to large angular scales across multiple frequency channels. The resulting Compton-y maps yield high-fidelity measurements of the tSZ signal, forming the backbone of modern studies into intracluster medium pressure profiles, cosmic baryon content, cluster-based cosmology, and secondary anisotropies of the cosmic microwave background (CMB).

1. Methodological Foundations and Component Separation

The creation of SPT+Planck Compton-y maps leverages the multi-frequency, multi-instrument approach for component separation, anchored in methodologies initially developed by Planck for robust separation of CMB, foregrounds, and secondary anisotropies (Collaboration et al., 2013). Four classes of algorithms are deployed in the Planck context:

• Commander-Ruler: A parametric, Bayesian pixel-space method, jointly fitting a full physical model for CMB and foregrounds using Gibbs sampling for spectral parameter estimation, followed by least-squares-amplified resolution enhancement ("Ruler").
• NILC (Needlet Internal Linear Combination): Conducts component separation in a wavelet basis, enabling spatial and angular adaptivity, exploiting the SZ spectral energy distribution to construct minimum-variance maps with unit response to tSZ while minimizing contaminants.
• SEVEM: Constructs internal templates from frequency differences to subtract foreground contamination in bands dominated by CMB or foregrounds.
• SMICA: Decomposes maps in harmonic space, fitting cross-frequency spectral covariance to optimize separation weights.

For SPT+Planck y-maps, these frameworks are adapted such that:

• Planck’s large-scale, full-sky information is combined in harmonic space with SPT’s small-scale, low-noise, high-resolution maps using inverse noise variance weighting (Chown et al., 2018).
• Band-specific linear combinations are used in Fourier/harmonic space, with explicit modeling of the spectral response and filtering/beam transfer functions of each instrument.
• Masking and filtering address problematic/missing modes (e.g., time-domain filtering of SPT) through additional ℓ–m-space weighting or filtering.

This architecture ensures both robust removal of primary CMB and Galactic foregrounds and minimization of extragalactic contaminants (notably, the cosmic infrared background, CIB) via flexible localization and explicit component nulling when required (Bleem et al., 2021, McCarthy et al., 2023).

2. Noise Characteristics and Foreground Control

Optimized SPT+Planck Compton-y maps are characterized by:

• Arcminute-level resolution (e.g., 1.25'–1.85' FWHM for highest-fidelity SPT+Planck maps (Bleem et al., 2021, Chown et al., 2018)).
• Substantially lower noise at small scales compared to Planck-only products, because of the high S/N from SPT at high-ℓ and the broad frequency leverage of Planck on large scales.
• Careful foreground mitigation, including:
  • Nulling the CMB and/or CIB components in the map linear combination (matrix-valued spectral response models).
  • Application of spatial and frequency-dependent confidence masks—examples include U73, which retains only sky regions with reliable component separation (Collaboration et al., 2013).
  • Explicit two-dimensional noise covariance modeling, handling spatially varying instrument and astrophysical noise.
  • Application of specialized filtering ("trough filters") to remove or down-weight contaminated or information-poor harmonic modes (notably for low-m SPT modes) (Bleem et al., 2021).

Residual foreground signals (dust, CIB, synchrotron, CO) are suppressed to levels where the dominant uncertainties are instrumental or cosmic variance. Galactic and extragalactic residuals are thoroughly characterized and cross-correlated with ancillary data (e.g., Herschel/SPIRE, radio source catalogs) to quantify systematic leakage (Bleem et al., 2021).

3. Construction, Validation, and Public Data Products

The construction pipeline for SPT+Planck Compton-y maps typically involves the following stages (Chown et al., 2018, Bleem et al., 2021):

1. Beam/Transfer Function Correction: Deconvolution of each band for its instrument beam and transfer function, ensuring harmonic-space consistency.
2. Harmonic-Space Inverse-Noise Weighting: For each (ℓ, m) mode, the estimate combines bands/instruments via weights

$$W^{\rm SPT}_{\ell m} = \frac{N^{\rm SPT}_{\ell m}{}^{-1}}{N^{\rm SPT}_{\ell m}{}^{-1} + N^{\rm Planck}_{\ell m}{}^{-1}}, \quad W^{\rm Planck}_{\ell m} = \frac{N^{\rm Planck}_{\ell m}{}^{-1}}{N^{\rm SPT}_{\ell m}{}^{-1} + N^{\rm Planck}_{\ell m}{}^{-1}}$$

1. Linear Combination/Component Separation: Application of the optimal LC/ILC weight vector (potentially matrix-valued if projecting out multiple contaminants), ensuring unit response to tSZ:

$$\vec{\psi} = \sigma_{\psi}^2 \mathbf{N}^{-1} \vec{f} R, \quad \sigma_{\psi}^{-2} = \vec{f}^T R^T \mathbf{N}^{-1} R \vec{f}$$

with R encoding the response and beam, and f the spectral signature of tSZ (Bleem et al., 2021).

1. Filtering and Inpainting: Removal of high-noise or missing modes, painting over the brightest sources to maintain noise stationarity and avoid ringing artifacts.
2. Validation: Multiple tests including one-point statistics (PDF, skewness), power spectra (auto/cross, ℓ-range agreement with models), nulling validation (via stacking, cluster detection performance), and cross-correlation with foreground tracers and simulations (Chown et al., 2018, Bleem et al., 2021).

The resulting data products include: minimum-variance Compton-y maps, CMB/kSZ-deprojected maps, noise PSDs, masks, beams, and transfer functions, provided in HEALPix or flat-sky formats (publicly at http://pole.uchicago.edu/public/data/sptsz_ymap and NASA/LAMBDA (Bleem et al., 2021)).

4. Scientific Applications and Impact

SPT+Planck Compton-y maps form the foundation for a diverse array of scientific analyses:

Cluster Astrophysics:

• Arcminute-resolution y-maps enable accurate stacking and measurement of radial pressure profiles across broad redshift and mass ranges.
• Joint SPT+Planck profile analyses can correct for instrument systematics, apply Malmquist bias corrections, and precisely constrain generalized NFW (gNFW) pressure profile parameters (Melin et al., 2023, Oppizzi et al., 2021).
• Stacked analyses reveal phenomena such as pressure deficits (interpreted as non-equilibrium electron–ion distributions at cluster boundaries) and accretion shocks well beyond the virial radius (Anbajagane et al., 2021).

Large-scale Structure and Cosmology:

• The angular power spectrum of the Compton-y maps provides direct constraints on cosmological parameters, notably S₈ and σ₈, and tests baryonic feedback models via comparison with hydrodynamical simulations (Tanimura et al., 2021, Dolag et al., 2015).
• Joint cross-correlations with galaxy surveys (e.g., DES Y3) enable measurement of the mean bias-weighted electron pressure ⟨bₕPₑ⟩, constraining hydrostatic mass bias and baryonic effects on the cosmic density field (Sánchez et al., 2022).
• Maps facilitate cross-correlations with CMB lensing for matter–gas connection studies (McCarthy et al., 2023), and probe the cosmic baryon budget outside galaxy clusters (the "missing baryons" problem).

Methodological Advances and Community Resources:

• The SPT+Planck methodology illustrates the synergy between high-resolution, deep ground-based surveys and full-sky, multi-frequency satellite data, setting the technical paradigm for future experiments (e.g., CMB-S4, Simons Observatory).
• Component separation pipelines (notably, public Python packages such as pyilc (McCarthy et al., 2023)) allow replication, validation, and extension by the wider community.

5. Systematic Effects, Limitations, and Ongoing Improvements

• Foreground Residuals: While the combined approach greatly mitigates CMB, Galactic, and CIB leakage, residual contamination—especially from faint dusty galaxies and radio sources—remains a limiting systematic at high multipoles and in the Galactic plane vicinity (Bleem et al., 2021, Chandran et al., 2023, McCarthy et al., 2023).
• Noise Covariance and Filtering: SPT’s time-domain filtering induces missing low-m modes that need to be compensated using Planck's large-scale coverage; specialized trough filters and inverse-variance weighting mitigate, but do not entirely eliminate, dependence on these corrections.
• Sample Selection Bias: Stacking and scaling analyses (e.g., average y-profiles) can be affected by selection bias—especially Malmquist bias in SPT-detected cluster samples—requiring explicit modeling and correction prior to global pressure profile estimation (Melin et al., 2023).
• Simulation Fidelity: Comparisons with cosmological simulations (e.g., Magneticum Pathfinder, Three Hundred project) highlight ongoing discrepancies at high ℓ and in low-mass systems, underscoring the importance of further improvements in baryonic feedback prescriptions and mass function calibrations (Dolag et al., 2015, Anbajagane et al., 2021).

6. Comparison with Planck-only and Alternative y-map Products

Contemporary Planck PR4-based y-maps, such as those constructed via the NILC or MILCA methods (Chandran et al., 2023, Chandran et al., 2023, McCarthy et al., 2023), demonstrate notable improvements in noise, foreground suppression, and systematic artifact control relative to the PR2 (2015) products. Unlike Planck-only maps (10′ resolution), SPT+Planck products retain full sensitivity to both arcminute and degree-scale modes, delivering superior pressure profile reconstruction at both core and outskirts of clusters (Melin et al., 2023). Public NILC/ILC pipelines now support deprojection of frequency-dependent contaminants (notably CIB), offering more flexible optimization for SZ science (McCarthy et al., 2023), and similar techniques have been extended to joint ACT+Planck products over large sky areas (Coulton et al., 2023).

7. Future Directions and Community Standards

The SPT+Planck Compton-y map paradigm sets the technical benchmark for secondary CMB anisotropy measurement. The approach is under continuous refinement as the community pushes for:

• Full-sky coverage at arcminute resolution by combining more ground-based data (ACT, SPT-3G) with Planck PR4/NPIPE.
• Deeper all-sky maps leveraging upcoming CMB-S4 and Simons Observatory data, with enhanced frequency coverage to further suppress foregrounds and probe lower-mass, higher-redshift galaxy clusters.
• Public pipelines (e.g., pyilc) and open-data formats fostering reproducibility, systematic error propagation studies, and machine learning-based astrophysical inference (e.g., CNN-based cluster mass estimation from Compton-y maps (Andres et al., 2022)).

In summary, SPT+Planck Compton-y maps represent the current state-of-the-art for tSZ studies, combining complementary instrumental advantages and advanced component separation to deliver low-noise, high-resolution measurements of the cosmic electron pressure field. These resources are central to contemporary cosmological and astrophysical investigations of baryonic physics, cluster thermodynamics, and the evolution of structure in the Universe.